The Role of the $t{\bar t}h$ Rest Frame in Direct Top-Quark Yukawa Coupling Measurements

This paper studies new possibilities to directly measure a hypothetical $CP$-odd (pseudoscalar) component in the top-quark Yukawa coupling. In particular, the role of the $t{\bar t} h$ center-of-mass rest frame in the associated production of a top pair and a $h$ boson at the LHC is explored. The $h$ boson is assumed to have both a $CP$-even (scalar) and a $CP$-odd coupling to the top quark. The relative strength of the scalar and pseudoscalar components is regulated by an angle $\alpha$. Observables sensitive to the nature of the top-quark Yukawa coupling are proposed. These observables are defined in terms of the transverse and longitudinal projections of $t$, $\bar{t}$ and $h$ momenta with respect to the beam axis in the $t{\bar t} h$ rest frame. Distributions differential with respect to those observables are evaluated up to NLO in QCD. These distributions are found to be sensitive to the $CP$ nature of the coupling. Dileptonic final states of the $t{\bar t} h$ system (with $h\rightarrow b\bar b$) are used, after fast DELPHES detector simulation and full event reconstruction through a kinematic fit, as a case study to test the observables' sensitivity to the $CP$ nature of the coupling. Confidence levels are presented as a function of the total integrated LHC luminosity for the case of exclusion of a pure $CP$-odd coupling against the Standard Model $CP$-even hypothesis. By using observables evaluated in the $t{\bar t} h$ system, the luminosity needed to directly probe the $CP$ properties of the top-quark Yukawa coupling at the High-Luminosity run of the LHC can be decreased by a few hundred inverse femtobarns, when compared to analyses that use observables in the laboratory rest frame. In addition, transverse momentum distributions of the $h$ boson and top quarks are found to provide no more discriminant power than a counting experiment. This work was supported by Fundacao para a Ciencia e Tecnologia, FCT (projects CERN/FIS-PAR/0034/2017, contract No. SFRH/BSAB/139747/2018 Ref CRM:0061260 and scholarship PD/BD/128231/2016). The in-house Monte-Carlo code which we developed and employed to evaluate the (differential) cross sections presented in this paper was run on the computer cluster of the Center for Theoretical Physics at the Physics Department of New York City College of Technology. This work was supported by the Professional Staff Congress-City University of New York Grants. No. 61085-00 49, No. 61151-00 49 and No. 62187-00 50.